Get A Mathematical Theory of Hints: An Approach to the PDF

By Prof. Dr. Jürg Kohlas, Dr. Paul-André Monney (auth.)

ISBN-10: 3540591761

ISBN-13: 9783540591764

ISBN-10: 3662016745

ISBN-13: 9783662016749

The topic of the e-book is an method of the modeling of and the reasoning less than uncertainty. It develops the Dempster-Shafer idea as a thought of the reliability of reasoning with doubtful arguments. a selected curiosity of this technique is that it yields a brand new synthesis and integration of common sense and chance thought. The reader will reap the benefits of a brand new view at uncertainty modeling which extends classical likelihood theory.

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Introductory Examples the two plausibility functions. It is easy to see that the combined plausibility function so far is then determined by pl(t) = min {pll(t),pl"(t)}. However, there may be values of a for which the above intersection of the a-cuts are empty. But these are clearly precision indices which are to be excluded, because they lead to an impossible conclusion. Let a* be the supremum of all a for which the intersection is not empty. e. the new distribution is uniform over the interval from O to a*.

This conclusion would have the reliability p(ei). If such arguments were selected for alI n measurements, then the condition Xl - el = X2 - e2 = ... 8) must be satisfied; otherwise the compound argument would be contradictory. A non-contradictory array (el, e2, ... , e n ) of arguments or errors such that Xi ei = i for aH i = 1,2, ... ,n is a combined argument for the quantity T to equal i. And it is the only one for this value t. 5 Measurement, Estimation and Diagnostics 21 where II k is the probability of no contradiction between the errors.

In fact, the duration may depend for example on the realization of a particular scenario about future meteorological conditions. For example, the possi bIe scenarios may be Wl = good weather, W2 = doudy, and W3 = bad weather. If durations are expressed in days, then we may take as the non-negative integers and for a particular activity T( Wl) could be the integer interval between 5 and 7, T(W2) between 6 and 9 and F(W3) between 8 and 12. If probabilities are given to the scenarios, then we have a hint for the durat ion of the activity.

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A Mathematical Theory of Hints: An Approach to the Dempster-Shafer Theory of Evidence by Prof. Dr. Jürg Kohlas, Dr. Paul-André Monney (auth.)


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